Gaussian measures of dilatations of convex symmetric sets

We prove that the inequality Psi(-1)(mu(tA)) greater than or equal to t Psi (-1)(mu(A)) holds for any centered Gaussian measure Cc on a separable Banac h space F, any convex, closed, symmetric set A subset of F and t greater th an or equal to 1, where Psi(x) = gamma(1)(-x, x) = (2 pi)(-1/2) integral(-x )(x) exp(-y(2)/2) dy. As an application, the best constants in comparison o f moments of Gaussian vectors are calculated.